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The CRESST experiment, located at Laboratori Nazionali del Gran Sasso inItaly, searches for dark matter particles via their elastic scattering offnuclei in a target material. The CRESST target consists of scintillatingCaWO$_4$ crystals, which are operated as cryogenic calorimeters at millikelvintemperatures. Each interaction in the CaWO$_4$ target crystal produces a phononsignal and a light signal that is measured by a second cryogenic calorimeter.Since the CRESST-II result in 2015, the experiment is leading the field ofdirect dark matter search for dark matter masses below 1.7\,GeV/$c^2$,extending the reach of direct searches to the sub-GeV/$c^2$ mass region. ForCRESST-III, whose Phase 1 started in July 2016, detectors have been optimizedto reach the performance required to further probe the low-mass region withunprecedented sensitivity. In this contribution the achievements of theCRESST-III detectors will be discussed together with preliminary results andperspectives of Phase 1.

First results on low-mass dark matter from the CRESST-III experiment